Subgroups — C₂×C₇₃×#2600 #32944307

Order 18688.

3502 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2600	C₂	1	16	yes	maximal, direct product factor
3	C₂×#397×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#394×C₇₃	C₂	1	2	yes	maximal, complemented
5	C₂×#392×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#388×C₇₃	C₂	1	2	yes	maximal, complemented
7	C₂×#387×C₇₃	C₂	1	2	yes	maximal, complemented
8	C₂×#386×C₇₃	C₂	1	2	yes	maximal, complemented
9	C₂×#385×C₇₃	C₂	1	2	yes	maximal, complemented
10	C₂×#381×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₇₃	C₂²	1	2	yes	—
12	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₇₃	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₇₃	—	2	16	no	—
16	C₂×C₄×D₄×C₇₃	C₂²	1	16	yes	complemented
17	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
27	C₂²×C₄²×C₇₃	C₂²	1	2	yes	—
28	#397×C₇₃	C₂²	1	8	yes	complemented
29	#394×C₇₃	C₂²	1	16	yes	complemented
30	#392×C₇₃	C₂²	1	8	yes	—
31	#388×C₇₃	C₂²	1	16	yes	complemented
32	#387×C₇₃	C₂²	1	16	yes	complemented
33	#386×C₇₃	C₂²	1	16	yes	complemented
34	#385×C₇₃	C₂²	1	16	yes	complemented
35	#381×C₇₃	C₂²	1	8	yes	complemented
36	C₂×#95×C₇₃	C₂²	1	2	yes	—
37	C₂×#95×C₇₃	C₂²	1	2	yes	—
38	C₂×#95×C₇₃	C₂²	1	2	yes	—
39	C₂×#95×C₇₃	C₂²	1	2	yes	—
40	C₂×#95×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×#95×C₇₃	C₂²	1	1	yes	characteristic
42	C₂⁵×C₇₃	C₂³	1	1	yes	characteristic
43	C₂⁵×C₇₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₇₃	—	2	8	no	—
45	C₂²×D₄×C₇₃	—	2	8	no	—
46	C₂²×D₄×C₇₃	—	2	8	no	—
47	C₂²×D₄×C₇₃	—	2	8	no	—
48	C₂²×D₄×C₇₃	—	4	2	no	—
49	C₂²×D₄×C₇₃	C₂³	1	8	yes	—
50	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
51	C₂³×C₄×C₇₃	—	2	8	no	—
52	C₂³×C₄×C₇₃	—	4	2	no	—
53	C₂³×C₄×C₇₃	—	4	2	no	—
54	C₂³×C₄×C₇₃	—	4	4	no	—
55	C₂³×C₄×C₇₃	—	4	4	no	—
56	C₂³×C₄×C₇₃	D₄	1	8	yes	complemented
57	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₇₃	C₂³	1	8	yes	—
65	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
66	C₄×D₄×C₇₃	—	2	64	no	—
67	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
68	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
69	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
70	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
71	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
72	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	4	2	no	—
78	C₂×C₂²⋊C₄×C₇₃	—	4	4	no	—
79	C₂×C₂²⋊C₄×C₇₃	—	4	2	no	—
80	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
81	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
82	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
83	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
84	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
87	C₂×C₄²×C₇₃	—	2	8	no	—
88	C₂×C₄²×C₇₃	C₂³	1	8	yes	—
89	#95×C₇₃	C₂³	1	8	yes	—
90	#95×C₇₃	C₂³	1	8	yes	—
91	#95×C₇₃	C₂³	1	8	yes	—
92	#95×C₇₃	C₂³	1	8	yes	—
93	#95×C₇₃	C₂³	1	4	yes	—
94	#95×C₇₃	C₂³	1	4	yes	—
95	C₂⁴×C₇₃	—	2	4	no	—
96	C₂⁴×C₇₃	—	2	4	no	—
97	C₂⁴×C₇₃	—	2	4	no	—
98	C₂⁴×C₇₃	—	2	4	no	—
99	C₂⁴×C₇₃	—	2	4	no	—
100	C₂⁴×C₇₃	—	2	4	no	—
101	C₂⁴×C₇₃	—	2	2	no	—
102	C₂⁴×C₇₃	—	2	2	no	—
103	C₂⁴×C₇₃	—	2	4	no	—
104	C₂⁴×C₇₃	—	2	4	no	—
105	C₂⁴×C₇₃	C₂×D₄	1	4	yes	—
106	C₂⁴×C₇₃	#41	1	8	yes	—
107	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
108	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
109	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
110	C₂×D₄×C₇₃	—	2	64	no	—
111	C₂×D₄×C₇₃	—	2	16	no	—
112	C₂×D₄×C₇₃	—	2	16	no	—
113	C₂×D₄×C₇₃	—	2	16	no	—
114	C₂×D₄×C₇₃	—	2	16	no	—
115	C₂×D₄×C₇₃	—	4	4	no	—
116	C₂×D₄×C₇₃	—	4	16	no	—
117	C₂²×C₄×C₇₃	—	2	4	no	—
118	C₂²×C₄×C₇₃	—	2	4	no	—
119	C₂²×C₄×C₇₃	—	2	4	no	—
120	C₂²×C₄×C₇₃	—	2	4	no	—
121	C₂²×C₄×C₇₃	—	2	4	no	—
122	C₂²×C₄×C₇₃	—	2	4	no	—
123	C₂²×C₄×C₇₃	—	2	4	no	—
124	C₂²×C₄×C₇₃	—	2	4	no	—
125	C₂²×C₄×C₇₃	—	2	4	no	—
126	C₂²×C₄×C₇₃	—	2	4	no	—
127	C₂²×C₄×C₇₃	—	2	4	no	—
128	C₂²×C₄×C₇₃	—	2	4	no	—
129	C₂²×C₄×C₇₃	—	2	4	no	—
130	C₂²×C₄×C₇₃	—	2	2	no	—
131	C₂²×C₄×C₇₃	—	2	4	no	—
132	C₂²×C₄×C₇₃	—	2	2	no	—
133	C₂²×C₄×C₇₃	—	2	4	no	—
134	C₂²×C₄×C₇₃	—	2	16	no	—
135	C₂²×C₄×C₇₃	—	4	16	no	—
136	C₂²×C₄×C₇₃	—	4	4	no	—
137	C₂²×C₄×C₇₃	—	4	4	no	—
138	C₂²×C₄×C₇₃	—	4	8	no	—
139	C₂²×C₄×C₇₃	—	4	8	no	—
140	C₂²×C₄×C₇₃	—	4	32	no	—
141	C₂²×C₄×C₇₃	C₂×D₄	1	8	yes	—
142	C₂²×C₄×C₇₃	C₂×D₄	1	16	yes	complemented
143	C₂²×C₄×C₇₃	#41	1	8	yes	—
144	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
151	C₄⋊C₄×C₇₃	—	2	16	no	—
152	C₄⋊C₄×C₇₃	—	2	16	no	—
153	C₄⋊C₄×C₇₃	—	4	4	no	—
154	C₂²⋊C₄×C₇₃	—	2	16	no	—
155	C₂²⋊C₄×C₇₃	—	2	16	no	—
156	C₂²⋊C₄×C₇₃	—	2	16	no	—
157	C₂²⋊C₄×C₇₃	—	2	16	no	—
158	C₂²⋊C₄×C₇₃	—	4	4	no	—
159	C₂²⋊C₄×C₇₃	—	4	8	no	—
160	C₂²⋊C₄×C₇₃	—	4	4	no	—
161	C₄²×C₇₃	—	2	16	no	—
162	C₂³×C₇₃	—	2	16	no	—
163	C₂³×C₇₃	—	2	16	no	—
164	C₂³×C₇₃	—	2	8	no	—
165	C₂³×C₇₃	—	2	16	no	—
166	C₂³×C₇₃	—	2	16	no	—
167	C₂³×C₇₃	—	2	4	no	—
168	C₂³×C₇₃	—	2	4	no	—
169	C₂³×C₇₃	—	2	4	no	—
170	C₂³×C₇₃	—	2	4	no	—
171	C₂³×C₇₃	—	2	4	no	—
172	C₂³×C₇₃	—	2	4	no	—
173	C₂³×C₇₃	—	2	2	no	—
174	C₂³×C₇₃	—	2	2	no	—
175	C₂³×C₇₃	—	2	4	no	—
176	C₂³×C₇₃	—	2	4	no	—
177	C₂³×C₇₃	—	4	8	no	—
178	C₂³×C₇₃	—	4	8	no	—
179	C₂³×C₇₃	—	4	4	no	—
180	C₂³×C₇₃	—	4	8	no	—
181	C₂³×C₇₃	—	4	8	no	—
182	C₂³×C₇₃	—	4	8	no	—
183	C₂³×C₇₃	—	4	4	no	—
184	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
185	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
186	C₂³×C₇₃	C₂×#41	1	8	yes	—
187	C₂³×C₇₃	C₂×#41	1	4	yes	—
188	C₂³×C₇₃	C₂×#41	1	4	yes	—
189	C₂³×C₇₃	H(5,𝔽₂)	1	2	yes	—
190	C₂³×C₇₃	H(5,𝔽₂)	1	2	yes	—
191	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
192	D₄×C₇₃	—	2	64	no	—
193	D₄×C₇₃	—	4	16	no	—
194	C₂×C₄×C₇₃	—	2	16	no	—
195	C₂×C₄×C₇₃	—	2	16	no	—
196	C₂×C₄×C₇₃	—	2	4	no	—
197	C₂×C₄×C₇₃	—	2	4	no	—
198	C₂×C₄×C₇₃	—	2	4	no	—
199	C₂×C₄×C₇₃	—	2	4	no	—
200	C₂×C₄×C₇₃	—	2	4	no	—
201	C₂×C₄×C₇₃	—	2	4	no	—
202	C₂×C₄×C₇₃	—	2	4	no	—
203	C₂×C₄×C₇₃	—	2	4	no	—
204	C₂×C₄×C₇₃	—	2	4	no	—
205	C₂×C₄×C₇₃	—	2	4	no	—
206	C₂×C₄×C₇₃	—	2	4	no	—
207	C₂×C₄×C₇₃	—	2	4	no	—
208	C₂×C₄×C₇₃	—	2	4	no	—
209	C₂×C₄×C₇₃	—	2	2	no	—
210	C₂×C₄×C₇₃	—	2	4	no	—
211	C₂×C₄×C₇₃	—	2	2	no	—
212	C₂×C₄×C₇₃	—	2	4	no	—
213	C₂×C₄×C₇₃	—	4	16	no	—
214	C₂×C₄×C₇₃	—	4	32	no	—
215	C₂×C₄×C₇₃	—	4	8	no	—
216	C₂×C₄×C₇₃	—	4	8	no	—
217	C₂×C₄×C₇₃	—	4	4	no	—
218	C₂×C₄×C₇₃	—	4	8	no	—
219	C₂×C₄×C₇₃	—	4	4	no	—
220	C₂×C₄×C₇₃	C₂²×D₄	1	8	yes	—
221	C₂×C₄×C₇₃	C₂×#41	1	8	yes	—
222	C₂²×C₇₃	—	2	8	no	—
223	C₂²×C₇₃	—	2	8	no	—
224	C₂²×C₇₃	—	2	4	no	—
225	C₂²×C₇₃	—	2	8	no	—
226	C₂²×C₇₃	—	2	8	no	—
227	C₂²×C₇₃	—	4	16	no	—
228	C₂²×C₇₃	—	4	32	no	—
229	C₂²×C₇₃	—	4	4	no	—
230	C₂²×C₇₃	—	4	4	no	—
231	C₂²×C₇₃	—	4	2	no	—
232	C₂²×C₇₃	—	4	4	no	—
233	C₂²×C₇₃	—	4	4	no	—
234	C₂²×C₇₃	—	4	4	no	—
235	C₂²×C₇₃	—	4	2	no	—
236	C₂²×C₇₃	#525	1	8	yes	—
237	C₂²×C₇₃	#534	1	4	yes	—
238	C₂²×C₇₃	#551	1	4	yes	—
239	C₂²×C₇₃	#553	1	8	yes	—
240	C₂²×C₇₃	#559	1	4	yes	—
241	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
242	C₂²×C₇₃	C₂²×#41	1	2	yes	—
243	C₂²×C₇₃	C₂²×#41	1	2	yes	—
244	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
245	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
246	C₄×C₇₃	—	2	8	no	—
247	C₄×C₇₃	—	2	8	no	—
248	C₄×C₇₃	—	4	4	no	—
249	C₄×C₇₃	—	4	4	no	—
250	C₄×C₇₃	—	4	2	no	—
251	C₄×C₇₃	—	4	4	no	—
252	C₄×C₇₃	—	4	2	no	—
253	C₂×#2600	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂×C₇₃	—	4	4	no	—
255	C₂×C₇₃	—	4	8	no	—
256	C₂×C₇₃	#2600	1	8	yes	direct product factor
257	C₂×C₇₃	C₂×#525	1	2	yes	—
258	C₂×C₇₃	C₂×#534	1	1	yes	characteristic
259	C₂×C₇₃	C₂×#551	1	1	yes	characteristic
260	C₂×C₇₃	C₂×#553	1	2	yes	—
261	C₂×C₇₃	C₂×#559	1	1	yes	characteristic
262	C₂²×C₄×D₄	C₂×C₇₃	1	2	yes	complemented
263	#2600	C₂×C₇₃	1	16	yes	direct product factor
264	C₂×#397	C₂×C₇₃	1	1	yes	characteristic, complemented
265	C₂×#394	C₂×C₇₃	1	2	yes	complemented
266	C₂×#392	C₂×C₇₃	1	1	yes	characteristic
267	C₂×#388	C₂×C₇₃	1	2	yes	complemented
268	C₂×#387	C₂×C₇₃	1	2	yes	complemented
269	C₂×#386	C₂×C₇₃	1	2	yes	complemented
270	C₂×#385	C₂×C₇₃	1	2	yes	complemented
271	C₂×#381	C₂×C₇₃	1	1	yes	characteristic, complemented
272	C₇₃	C₂×#2600	1	1	yes	characteristic, direct product factor, Sylow
273	C₂³×D₄	C₂²×C₇₃	1	2	yes	—
274	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
275	C₂⁴×C₄	C₂²×C₇₃	1	2	yes	—
276	C₂⁴×C₄	C₂²×C₇₃	1	1	yes	characteristic
277	C₂×C₄×D₄	—	2	16	no	—
278	C₂×C₄×D₄	C₂²×C₇₃	1	16	yes	complemented
279	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
281	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
282	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
283	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
284	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
285	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
286	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
287	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
288	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
289	C₂²×C₄²	C₂²×C₇₃	1	2	yes	—
290	#397	C₂²×C₇₃	1	8	yes	complemented
291	#394	C₂²×C₇₃	1	16	yes	complemented
292	#392	C₂²×C₇₃	1	8	yes	—
293	#388	C₂²×C₇₃	1	16	yes	complemented
294	#387	C₂²×C₇₃	1	16	yes	complemented
295	#386	C₂²×C₇₃	1	16	yes	complemented
296	#385	C₂²×C₇₃	1	16	yes	complemented
297	#381	C₂²×C₇₃	1	8	yes	complemented
298	C₂×#95	C₂²×C₇₃	1	1	yes	characteristic
299	C₂×#95	C₂²×C₇₃	1	2	yes	—
300	C₂×#95	C₂²×C₇₃	1	2	yes	—
301	C₂×#95	C₂²×C₇₃	1	1	yes	characteristic
302	C₂×#95	C₂²×C₇₃	1	2	yes	—
303	C₂×#95	C₂²×C₇₃	1	2	yes	—
304	C₂⁵	C₂³×C₇₃	1	1	yes	characteristic
305	C₂⁵	C₂³×C₇₃	1	2	yes	—
306	C₂²×D₄	—	2	8	no	—
307	C₂²×D₄	—	2	8	no	—
308	C₂²×D₄	—	2	8	no	—
309	C₂²×D₄	—	2	8	no	—
310	C₂²×D₄	—	4	2	no	—
311	C₂²×D₄	C₂³×C₇₃	1	8	yes	—
312	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
313	C₂³×C₄	—	2	8	no	—
314	C₂³×C₄	—	4	2	no	—
315	C₂³×C₄	—	4	2	no	—
316	C₂³×C₄	—	4	4	no	—
317	C₂³×C₄	—	4	4	no	—
318	C₂³×C₄	D₄×C₇₃	1	8	yes	complemented
319	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
321	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
322	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
323	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
325	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
326	C₂³×C₄	C₂³×C₇₃	1	8	yes	—
327	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
328	C₄×D₄	—	2	64	no	—
329	C₂×C₄⋊C₄	—	2	8	no	—
330	C₂×C₄⋊C₄	—	2	8	no	—
331	C₂×C₄⋊C₄	—	4	2	no	—
332	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
333	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
334	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
335	C₂×C₂²⋊C₄	—	2	8	no	—
336	C₂×C₂²⋊C₄	—	2	8	no	—
337	C₂×C₂²⋊C₄	—	2	8	no	—
338	C₂×C₂²⋊C₄	—	2	8	no	—
339	C₂×C₂²⋊C₄	—	4	2	no	—
340	C₂×C₂²⋊C₄	—	4	4	no	—
341	C₂×C₂²⋊C₄	—	4	2	no	—
342	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
349	C₂×C₄²	—	2	8	no	—
350	C₂×C₄²	C₂³×C₇₃	1	8	yes	—
351	#95	C₂³×C₇₃	1	8	yes	—
352	#95	C₂³×C₇₃	1	8	yes	—
353	#95	C₂³×C₇₃	1	8	yes	—
354	#95	C₂³×C₇₃	1	8	yes	—
355	#95	C₂³×C₇₃	1	4	yes	—
356	#95	C₂³×C₇₃	1	4	yes	—
357	C₂⁴	—	2	4	no	—
358	C₂⁴	—	2	4	no	—
359	C₂⁴	—	2	4	no	—
360	C₂⁴	—	2	4	no	—
361	C₂⁴	—	2	4	no	—
362	C₂⁴	—	2	4	no	—
363	C₂⁴	—	2	2	no	—
364	C₂⁴	—	2	2	no	—
365	C₂⁴	—	2	4	no	—
366	C₂⁴	—	2	4	no	—
367	C₂⁴	C₂×D₄×C₇₃	1	4	yes	—
368	C₂⁴	#41×C₇₃	1	8	yes	—
369	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
370	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
371	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
372	C₂×D₄	—	2	64	no	—
373	C₂×D₄	—	2	16	no	—
374	C₂×D₄	—	2	16	no	—
375	C₂×D₄	—	2	16	no	—
376	C₂×D₄	—	2	16	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	—	4	16	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	16	no	—
397	C₂²×C₄	—	4	16	no	—
398	C₂²×C₄	—	4	4	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	4	8	no	—
401	C₂²×C₄	—	4	8	no	—
402	C₂²×C₄	—	4	32	no	—
403	C₂²×C₄	C₂×D₄×C₇₃	1	8	yes	—
404	C₂²×C₄	C₂×D₄×C₇₃	1	16	yes	complemented
405	C₂²×C₄	#41×C₇₃	1	8	yes	—
406	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
408	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
411	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
413	C₄⋊C₄	—	2	16	no	—
414	C₄⋊C₄	—	2	16	no	—
415	C₄⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	2	16	no	—
417	C₂²⋊C₄	—	2	16	no	—
418	C₂²⋊C₄	—	2	16	no	—
419	C₂²⋊C₄	—	2	16	no	—
420	C₂²⋊C₄	—	4	4	no	—
421	C₂²⋊C₄	—	4	8	no	—
422	C₂²⋊C₄	—	4	4	no	—
423	C₄²	—	2	16	no	—
424	C₂³	—	2	16	no	—
425	C₂³	—	2	16	no	—
426	C₂³	—	2	8	no	—
427	C₂³	—	2	16	no	—
428	C₂³	—	2	16	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	4	8	no	—
440	C₂³	—	4	8	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	8	no	—
443	C₂³	—	4	8	no	—
444	C₂³	—	4	8	no	—
445	C₂³	—	4	4	no	—
446	C₂³	C₂²×D₄×C₇₃	1	4	yes	—
447	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
448	C₂³	C₂×#41×C₇₃	1	8	yes	—
449	C₂³	C₂×#41×C₇₃	1	4	yes	—
450	C₂³	C₂×#41×C₇₃	1	4	yes	—
451	C₂³	H(5,𝔽₂)×C₇₃	1	2	yes	—
452	C₂³	H(5,𝔽₂)×C₇₃	1	2	yes	—
453	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
454	D₄	—	2	64	no	—
455	D₄	—	4	16	no	—
456	C₂×C₄	—	2	16	no	—
457	C₂×C₄	—	2	16	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	4	16	no	—
476	C₂×C₄	—	4	32	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	8	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	8	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	C₂²×D₄×C₇₃	1	8	yes	—
483	C₂×C₄	C₂×#41×C₇₃	1	8	yes	—
484	C₂²	—	2	8	no	—
485	C₂²	—	2	8	no	—
486	C₂²	—	2	8	no	—
487	C₂²	—	2	8	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	16	no	—
495	C₂²	—	4	32	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	4	no	—
498	C₂²	#525×C₇₃	1	8	yes	—
499	C₂²	#534×C₇₃	1	4	yes	—
500	C₂²	#551×C₇₃	1	4	yes	—
501	C₂²	#553×C₇₃	1	8	yes	—
502	C₂²	#559×C₇₃	1	4	yes	—
503	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
504	C₂²	C₂²×#41×C₇₃	1	2	yes	—
505	C₂²	C₂²×#41×C₇₃	1	2	yes	—
506	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
507	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
508	C₄	—	2	8	no	—
509	C₄	—	2	8	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	4	no	—
514	C₄	—	4	4	no	—
515	C₂	—	4	8	no	—
516	C₂	—	4	4	no	—
517	C₂	C₇₃×#2600	1	8	yes	direct product factor
518	C₂	C₂×#525×C₇₃	1	2	yes	—
519	C₂	C₂×#534×C₇₃	1	1	yes	characteristic
520	C₂	C₂×#551×C₇₃	1	1	yes	characteristic
521	C₂	C₂×#553×C₇₃	1	2	yes	—
522	C₂	C₂×#559×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂×#392×C₇₃	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂²×C₄×D₄×C₇₃	C₂	semidirect
2. C₇₃×#2600	C₂	direct (N × H)
3. C₂×#397×C₇₃	C₂	semidirect
4. C₂×#394×C₇₃	C₂	semidirect
6. C₂×#388×C₇₃	C₂	semidirect
7. C₂×#387×C₇₃	C₂	semidirect
8. C₂×#386×C₇₃	C₂	semidirect
9. C₂×#385×C₇₃	C₂	semidirect
10. C₂×#381×C₇₃	C₂	semidirect
16. C₂×C₄×D₄×C₇₃	C₂²	semidirect
28. #397×C₇₃	C₂²	semidirect
29. #394×C₇₃	C₂²	semidirect
31. #388×C₇₃	C₂²	semidirect
32. #387×C₇₃	C₂²	semidirect
33. #386×C₇₃	C₂²	semidirect
34. #385×C₇₃	C₂²	semidirect
35. #381×C₇₃	C₂²	semidirect
56. C₂³×C₄×C₇₃	D₄	semidirect
142. C₂²×C₄×C₇₃	C₂×D₄	semidirect
253. C₂×#2600	C₇₃	direct (N × H)
256. C₂×C₇₃	#2600	direct (N × H)
262. C₂²×C₄×D₄	C₂×C₇₃	semidirect
263. #2600	C₂×C₇₃	direct (N × H)
264. C₂×#397	C₂×C₇₃	semidirect
265. C₂×#394	C₂×C₇₃	semidirect
267. C₂×#388	C₂×C₇₃	semidirect
268. C₂×#387	C₂×C₇₃	semidirect
269. C₂×#386	C₂×C₇₃	semidirect
270. C₂×#385	C₂×C₇₃	semidirect
271. C₂×#381	C₂×C₇₃	semidirect
272. C₇₃	C₂×#2600	direct (N × H)
278. C₂×C₄×D₄	C₂²×C₇₃	semidirect
290. #397	C₂²×C₇₃	semidirect
291. #394	C₂²×C₇₃	semidirect
293. #388	C₂²×C₇₃	semidirect
294. #387	C₂²×C₇₃	semidirect
295. #386	C₂²×C₇₃	semidirect
296. #385	C₂²×C₇₃	semidirect
297. #381	C₂²×C₇₃	semidirect
318. C₂³×C₄	D₄×C₇₃	semidirect
404. C₂²×C₄	C₂×D₄×C₇₃	semidirect
517. C₂	C₇₃×#2600	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄×D₄×C₇₃	2
C₇₃×#2600	2
C₂×#397×C₇₃	2
C₂×#394×C₇₃	2
C₂×#392×C₇₃	2
C₂×#388×C₇₃	2
C₂×#387×C₇₃	2
C₂×#386×C₇₃	2
C₂×#385×C₇₃	2
C₂×#381×C₇₃	2
C₂×#2600	73

Subgroups — C2×C73×#2600 #32944307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#2600 #32944307